Still, hunting and fishing are usually the 2nd and 3rd worst starting techs. I don't like going straight to the expensive AH without mining or agriculture, because then your worker will have nothing to do (unless you have at least two livestock resources, which isn't very common). Hunting and fishing can be pretty awkward.
I freely admit that I'm not the most practiced of players (still getting to grips with Prince), but AH seems useful for unlocking horses and therefore Chariots. I tend to have far more luck with chariot rushes than with axe rushes, though that may just come down to more consistently finding nearby horses than nearby copper. Chariots are also much more useful for exploring and fending off barbarians in my experience.
Granted you'll want both AH and BW for a chariot rush so you can chop the chariots.